Problem 28 - College Physics

Question

Driving a jet-powered car, Royal Air Force pilot Andy Green broke the sound barrier on land for the first time and achieved a record land speed of more than \(763 \mathrm{mi} / \mathrm{h}\) in Black Rock Desert, Nevada, on October 15,1997 (vFig. 1.15). (a) What is this speed expressed in \(\mathrm{m} / \mathrm{s}\) ? (b) How long would it take the jet-powered car to travel the length of a 300 - \(\mathrm{ft}\) football field at this speed?

Step-by-Step Solution

Answer

The speed is approximately 341.34 m/s, and it takes about 0.268 seconds to travel a 300-ft field.

Step 1: Understand Unit Conversion

To convert the speed from miles per hour to meters per second, we need to know the conversion factors: 1 mile is approximately 1609.34 meters, and 1 hour is 3600 seconds. We'll use these to convert 763 miles per hour to meters per second.

Step 2: Convert Speed to Meters Per Second

We know that 1 mile = 1609.34 meters and 1 hour = 3600 seconds. To convert 763 mi/h to m/s, calculate:\[763 \text{ mi/h} \times \frac{1609.34}{1} \times \frac{1}{3600} \approx 341.338 \text{ m/s}\]

Step 3: Convert Field Length to Meters

We need the length of the football field in meters for speed calculation. The field is 300 feet long, and 1 foot is approximately 0.3048 meters. So convert the length:\[300 \text{ ft} \times 0.3048 \approx 91.44 \text{ m}\]

Step 4: Calculate Time to Travel Football Field

Now, using the speed and the length of the football field in meters, calculate the time it would take to cover that distance. Time is calculated using the formula \( \text{time} = \frac{\text{distance}}{\text{speed}} \). Plug in the values:\[\text{time} = \frac{91.44}{341.338} \approx 0.268 \text{ seconds}\]

Step 5: Conclusion

The speed of 763 miles per hour converts to approximately 341.34 meters per second. It would take the jet-powered car approximately 0.268 seconds to travel the length of a 300-ft football field at this speed.

Key Concepts

Miles per hour to meters per second

When converting speeds from miles per hour (mph) to meters per second (m/s), it's essential to understand the basic conversion factors. This conversion is often required in physics to standardize units across calculations, as the metric system is widely used in scientific contexts.
To convert:

• First, know that 1 mile equals about 1609.34 meters.
• Similarly, there are 3600 seconds in an hour.

Using these factors helps us convert any speed given in mph to m/s effectively. For example, if a car is traveling at 763 mph, you would multiply 763 by 1609.34 to convert the distance to meters and then divide by 3600 to convert the time to seconds. The calculation can be represented in the equation: \[763 \text{ mi/h} \times \frac{1609.34}{1} \times \frac{1}{3600} \approx 341.338 \text{ m/s}\]
This equation simplifies the process and helps ensure accuracy.

Football field length conversion

Field lengths, especially in sports like football, are commonly measured in feet rather than meters. To perform accurate calculations in physics, such as speed and distance maneuvers, converting feet to meters is necessary.

Consider that 1 foot is approximately 0.3048 meters. So, if you have a field that is 300 feet long, its length in meters can be calculated as follows:

• Multiply the length in feet by the conversion factor: 300 feet \( \times 0.3048 \).

This gives:\[300 \times 0.3048 \approx 91.44 \text{ meters}\]Transforming measurements from feet to meters provides consistency within the metric system, aiding in clearer and more accurate physics computations.

Speed and distance calculation

In physics, calculating the time it takes for an object to travel a certain distance using its speed is foundational. This step is crucial, whether dealing with cars, planes, or spaceships. The general formula is: \[ \text{time} = \frac{\text{distance}}{\text{speed}} \] Once you understand the distance in meters and the speed in meters per second, it's straightforward. Using the example of a jet-powered car with a speed of approximately 341.34 m/s and the football field length of 91.44 meters, you can calculate the time as follows: \[\text{time} = \frac{91.44}{341.338} \approx 0.268 \text{ seconds}\] This result tells us how quick the journey is, illustrating how fast the vehicle travels relative to the distance. Understanding this concept is crucial for solving many real-world physics problems.

Physics problem-solving steps

Approaching physics problems methodically is key to successful resolution. Begin by identifying what is given and what needs to be found. For unit conversion problems, knowing the correct conversion factors is essential.

Follow these general steps:

• Understand the Problem: Clearly define what you're trying to find. Here, you're asked to convert speeds and lengths and find the time taken to travel a distance.
• Gather Information: Identify the known quantities and necessary conversion units.
• Perform the Calculations: Carry out the conversion calculations methodically, using the correct units.
• Double Check Your Work: Make sure your units match and the math is correct.

By structuring your approach, physics problems become manageable and logical, leading to solutions that are consistent and accurate.